Find the general solution of the following equation valid near the origin: (1+4x²) y¹¹-8y=0 |`ymag(1−4x²)+a[{x-22²2-²_7"}]} Option 1 y=(1+4x²) +-√x+Ē (−1)²+¹+3+3=1 44²-1 Option 3 yma Option 2 (−1)²₂ ³+1 Option 4 44²-1 2³2+1 (x(+²)+(-²²] a ₂ (1+4 4².

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Find the general solution of the following equation valid near the origin:

Find the general solution of the following equation valid near the origin:
(1+4x²) y'' - 8y=0
|ymag(1-4x²) + √2-2223;2+1] =y=(1-40²) + [+ (-1)²23,2-1
2
Option 1
y=(1+4x²) + √(x + (−1)4+1-31, 2+1
*
4k²-1
Option 3
Option 2
22424.
y=a (1+4x²)+a[{x-2 ²4/³2-1"]
Option 4
Transcribed Image Text:Find the general solution of the following equation valid near the origin: (1+4x²) y'' - 8y=0 |ymag(1-4x²) + √2-2223;2+1] =y=(1-40²) + [+ (-1)²23,2-1 2 Option 1 y=(1+4x²) + √(x + (−1)4+1-31, 2+1 * 4k²-1 Option 3 Option 2 22424. y=a (1+4x²)+a[{x-2 ²4/³2-1"] Option 4
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